Pair Ranking. Problem Domain Analysis CHAPTER 9

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1 CHAPTER 9 Pair Ranking Pair ranking is a voting system developed in 1987 by Nicolaus Tideman. It selects a single winner using votes that express preferences. It can also be used to create a sorted list of winners. Problem Domain Analysis Let s say we need to rank four choices: A, B, C, and D. To pair-rank these choices, we list them in a column, one beneath the other: Choice B Choice C Choice D We then ask: Which is better, A or B? We mark the choice we decide is better say, B. Choice B Choice C Choice D We then ask why B is better and record our reasoning separately. The voting yields only our preference if we don t ask why we favor B over A. The question identifies the rationale, which is the most important part of the process. Now, which is better, A or C? We mark C and record our reasoning. Choice B Choice C Choice D Which is better, A or D? We mark D and record our reasoning. Choice B Choice C Choice D Bala Paranj 2017 B. Paranj, Test Driven Development in Ruby, DOI / _9 277

2 Which is better, B or C? We mark B and record our reasoning. Choice B Choice C Choice D Which is better, B or D? We mark B and record our reasoning. Choice B Choice C Choice D Which is better, C or D? We mark C and record our reasoning. Choice B Choice C Choice D We systematically compare each item with every other item. Choice B has three votes, C has two votes, D has one, and A has none. The item with the most votes is ranked first. In this case, that s choice B. Table 9-1 summarizes the result. Table 9-1. Pair-Ranking Result Choices Votes Ranking A 0 4 B 3 1 C 2 2 D 1 3 If two items up with the same number of votes, we rank the two items head to head to break the tie. The solution domain analysis, designing test cases, and developing the solution driven by tests are left as an exercise for the reader. Solution The following is one way to solve the problem. Create a pair_rank.rb file with the following code: module PairRank # Value Object # - Pair - Consists of two options # - Choice - Selected option from a given pair # - Criteria - Rationale for the preference. Why was the choice was made? class RationalChoice attr_reader :choice, :criteria, :pair 278

3 def initialize(pair, choice, = = = pair def to_s "You selected #{@choice} because of #{@criteria} for #{@pair}" class Combination def = = -1 def += class PairRank attr_reader :decisions def = = = = Combination.new(@options) def def def def tied_pair return [] if zeros? find_tie 279

4 280 def break_tie(pair, choice, criteria) make_rational_choice(pair, choice, criteria) def make_rational_choice(pair, choice, criteria) rc = RationalChoice.new(pair, choice, criteria) make(rc) private # All choices with 0 scores mean the pair-ranking process has not begun def zeros? list choice score_for(choice)} list.uniq == [0] def tie(combination) first = score_for(combination[0]) second = score_for(combination[1]) first == second def make(rational_choice) store(rational_choice) vote_for(rational_choice) def has_tie?!tied_pair.empty? def += 1 # For display at the of the pair-ranking process def << rational_choice def find_tie result = [] combinations.each do combination if tie(combination) result = combination break result

5 Create combination_test.rb as shown here: require 'minitest/autorun' require_relative pair_rank class CombinationTest < Minitest::Test include PairRank def test_get_first_pair_given_options c = Combination.new(options) result = assert_equal ['A', 'B'], result def test_get_second_pair_given_options c = Combination.new(options) result = assert_equal ['A', 'C'], result def test_get_third_pair_given_options c = Combination.new(options) result = assert_equal ['B', 'C'], result def test_get_pair_when_there_is_no_pair c = Combination.new(options) result = assert_equal nil, result 281

6 Create pair_rank_test.rb as shown here: require 'minitest/autorun' require_relative pair_rank class PairRankTest < Minitest::Test include PairRank def test_score_is_zero_for_the_element_that_did_not_get_vote options = [] result = pr.score_for('a') assert_equal 0, result def test_first_combination result = pr.combination assert_equal ['A', 'B'], result def test_second_combination pr.combination result = pr.combination assert_equal ['A', 'C'], result def test_in_the_beginning_all_scores_are_zero_so_its_not_a_tie options = ['A', 'B', 'C', 'D'] result = pr.tied_pair assert_equal [], result def test_complete_session_when_there_is_no_tie criteria = 'test' choice = 'B' 282

7 assert_equal 2, pr.score_for('a') assert_equal 1, pr.score_for('b') assert_equal 0, pr.score_for('c') def test_score_complete_session_where_there_are_ties criteria = 'test' choice = 'C' choice = 'B' assert_equal 1, pr.score_for('a') assert_equal 1, pr.score_for('b') assert_equal 1, pr.score_for('c') def test_get_tie_for_a_complete_session_when_there_are_ties criteria = 'test' choice = 'C' choice = 'B' assert_equal ['A', 'B'], pr.tied_pair def test_process_ties_for_a_complete_session_when_there_are_ties criteria = 'test' choice = 'C' 283

8 choice = 'B' pr.break_tie(pr.tied_pair, 'A', criteria) assert_equal ['B', 'C'], pr.tied_pair pr.break_tie(pr.tied_pair, 'B', criteria) assert_equal ['A', 'B'], pr.tied_pair pr.break_tie(pr.tied_pair, 'A', criteria) assert_equal [], pr.tied_pair def test_rational_choice_custom_string rc = RationalChoice.new('pair', 'choice', 'criteria') expected = "You selected choice because of criteria for pair" result = rc.to_s assert_equal expected, result Summary In this chapter, we discussed pair ranking and saw one way to code the solution. The concepts found in the domain, such as choice, rationale, and so on, are carried over to the code. We did this deliberately to reduce the semantic gap between the requirements and the code. 284

The Pairwise-Comparison Method

The Pairwise-Comparison Method Lecture 10 Section 1.5 Robb T. Koether Hampden-Sydney College Mon, Sep 11, 2017 Robb T. Koether (Hampden-Sydney College) The Pairwise-Comparison Method Mon, Sep 11, 2017